Bernoulli, Jacob (1695). "Explicationes, Annotationes & Additiones ad ea, quae in Actis sup. anni de Curva Elastica, Isochrona Paracentrica, & Velaria, hinc inde memorata, & paratim controversa legundur; ubi de Linea mediarum directionum, alliisque novis". Acta Eruditorum.. Cited in Hairer, Nørsett & Wanner (1993).
Hairer, Ernst; Nørsett, Syvert Paul; Wanner, Gerhard (1993). Solving ordinary differential equations I: Nonstiff problems. Berlin, New York: Springer-Verlag. ISBN978-3-540-56670-0..
ดูเพิ่ม
Bernoulli equation on PlanetMath
Differential equation on PlanetMath
Index of differential equations on PlanetMath
สิงหาคม 17, 2021
สมการเช, งอน, นธ, แบร, ลล, บทความน, างอ, งคร, สต, กราช, คร, สต, ทศวรรษ, คร, สต, ศตวรรษ, งเป, นสาระสำค, ญของเน, อหา, ในคณ, ตศาสตร, สมการเช, งอน, นธ, สาม, ในร, ปแบบ, displaystyle, เร, ยกว, สมการแบร, ลล, งกฤษ, bernoulli, equation, เม, displaystyle, งสมการน, งช, อ. bthkhwamnixangxingkhristskrach khristthswrrs khriststwrrs sungepnsarasakhykhxngenuxha inkhnitsastr smkarechingxnuphnthsamy inrupaebb y P x y Q x y n displaystyle y P x y Q x y n eriykwa smkaraebrnulli xngkvs Bernoulli equation emux n 1 displaystyle n neq 1 sungsmkarnitngchuxtam yakhxb aebrnulli Jakob Bernoulli phusungnaesnxsmkarrupaebbniiwinpi kh s 1695 Bernoulli 1695 smkaraebrnulli nnmikhwamnasnicephraasmkarechingxnuphnthimechingesnthi nonlinear differential equations miphltxbaemntrng exact solution enuxha 1 twxyang 1 1 twxyangthi 1 1 2 twxyangthi 2 2 karopraekrmin Math Lab 3 xangxing 4 duephimtwxyang aekikhtwxyangthi 1 aekikh phicarna y 2 y sin x y 2 sin x displaystyle y 2y operatorname sin x y 2 operatorname sin x hartlxdthngsmkar y y 2 2 sin x y 3 sin x displaystyle frac y y 2 frac 2 operatorname sin x y 3 operatorname sin x ih w 1 y 3 displaystyle w frac 1 y 3 emuxthakarhaxnuphnthcaidwa w w 6 sin x 3 sin x displaystyle w w6 operatorname sin x 3 operatorname sin x thakarhapriphnth w e 6 cos x 1 2 e 6 cos x C 1 2 C e 6 cos x displaystyle w e 6 operatorname cos x left frac 1 2 e 6 operatorname cos x C right frac 1 2 Ce 6 operatorname cos x enuxngcak w y 3 displaystyle w y 3 dngnn y displaystyle y mikhaethakb y 3 1 2 C e 6 cos x displaystyle y 3 sqrt frac 1 2 Ce 6 operatorname cos x twxyangthi 2 aekikh phicarnasmkaraebrnulli y 2 y x x 2 y 2 displaystyle y frac 2y x x 2 y 2 odychdecn y 0 displaystyle y 0 epnhnunginphllphth emuxhardwy y 2 displaystyle y 2 caid y y 2 2 x y 1 x 2 displaystyle y y 2 frac 2 x y 1 x 2 emuxepliyntwaepridrupaebbsmkarihm w 1 y displaystyle w frac 1 y w y y 2 displaystyle w frac y y 2 w 2 x w x 2 displaystyle w frac 2 x w x 2 sungsamarthhaaeksmkaridodyichtwprakxbpriphnth M x e 2 1 x d x e 2 ln x x 2 displaystyle M x e 2 int frac 1 x dx e 2 ln x x 2 khundwy M x displaystyle M x w x 2 2 x w x 4 displaystyle w x 2 2xw x 4 odythi dansaykhuxxnuphnthkhxng w x 2 displaystyle wx 2 daeninkarhapriphnththngsxngkhangkhxngsmkarcaidsmkar w x 2 d x x 4 d x displaystyle int wx 2 dx int x 4 dx w x 2 1 5 x 5 C displaystyle wx 2 frac 1 5 x 5 C 1 y x 2 1 5 x 5 C displaystyle frac 1 y x 2 frac 1 5 x 5 C phllphth y displaystyle y khux y 5 x 2 x 5 C displaystyle y frac 5x 2 x 5 C aela y 0 displaystyle y 0 karopraekrmin Math Lab aekikherasamarththakartrwcsxbkbinopraekrmaemtaelb MATLAB odyich symbolic toolbox odykarichrhsdngkhanglangni x dsolve Dy 2 y x x 2 y 2 x ihphltxbthngsxng 1 0 x 2 x 5 5 C1 xangxing aekikh duephimetimidcak solution ody WolframAlpha en odythiphltxb y 0 displaystyle y 0 caimaesdngphlephraaepnkrnichdaecng trivial case xyuaelw Bernoulli Jacob 1695 Explicationes Annotationes amp Additiones ad ea quae in Actis sup anni de Curva Elastica Isochrona Paracentrica amp Velaria hinc inde memorata amp paratim controversa legundur ubi de Linea mediarum directionum alliisque novis Acta Eruditorum Cited in Hairer Norsett amp Wanner 1993 Hairer Ernst Norsett Syvert Paul Wanner Gerhard 1993 Solving ordinary differential equations I Nonstiff problems Berlin New York Springer Verlag ISBN 978 3 540 56670 0 duephim aekikhBernoulli equation on PlanetMath Differential equation on PlanetMath Index of differential equations on PlanetMathekhathungcak https th wikipedia org w index php title smkarechingxnuphnthaebrnulli amp oldid 8852752, wikipedia, วิกิ หนังสือ, หนังสือ, ห้องสมุด,
